Can someone help me with this math problem please?

Question

Solve the system using the elimination method.

{x+10y=12

{-2x+5y=2

Answer 1

Using Elimination Method

 

x+10y=12

-2x+5y=2

 

to get the value of x we make the y equal

x + 10y=12

-2(-2x+5y=2)

 

thus....

   x+10y=12

  4x-10y=-4    We can add

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5x       = 8....to get x divide both sides by 5

5x/5=8/5

 

x=8/5

 

To get y, we can make x equal....

2(x+10y=12)

-2x+5y=2

thus....

 

 2x+20y=24

-2x+5y=2    We can add(remember rules of add/subtract negative nos)

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      25y=26....to get y divide both sides by 25

25y/25=26/25

y=26/25

 

x=8/5, y=26/25

 

To check: substitute value of x and y

8/5+10(26/25)=12

1.6+10(1.04)=12

1.6+10.4=12

12=12...yes

 

-2(8/5)+5(26/25)=2

-2(1.6)+5(1.04)=2

-3.2+5.2=2

2=2...yes

 

Answer 2

You want to answer this question by adding the two equations up along the columns such that one variable is eliminated, leaving the other variable. Once you have a value you can substitute that value back into an equation to get the other variable you just eliminated.

 

First, we should notice that we cannot currently add the two equations and eliminate a variable. However, we could take a multiple of an equation and then add.

 

If we multiply the first equation by 2, we will get {2x +20y = 24}. Now we can add equation 2 with equation 1.

 

{2x + 20y = 24

{-2x + 5y = 2

 

0x + 25y = 26

 

25y = 26

 

y = 26/25

 

Since x was eliminated, we could easily solve the remaining equation with only one variable.

 

Now, we will substitute y back into an equation to get x.

 

-2x + 5(26/25) = 2

 

-2x + 26/5 = 2

 

-2x = -16/5

 

x = 8/5

 

So our solution to the system is (8/5, 26/25)